is the image of f. is the kernal of f.
Let f: M ---> N be a R module homomorphism
P and Q are submodules of M and N respectively.
Show that:
(i) f(P) ={ f(p): p belongs to P} is a submodule of N
(ii) f^(-1)(Q) ={ m in M: f(m) belongs to Q} is a submodule of M
(iii) What are f(M) and f^(-1)(0)?
I have already proved part (i) and (ii)
My problem is part (iii). I don't know how to do it, it looks easy but I think it is a trick question. So, I have to bother you to help me on part(iii)
Thank you in advanced